# Modal analysis

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Car's door attached to an electromagnetic shaker.
A photograph showing the test set-up of a MIMO test on a wind turbine rotor. The blades are excited using three mechanical shakers and the response is measured using 12 accelerometers mounted to Blade 3; in the next stage of the test, the accelerometers can be moved to Blade 2 and 3 to measure response at those locations.[1]

Modal analysis is the study of the dynamic properties of structures under vibrational excitation.

Modal analysis is the field of measuring and analysing the dynamic response of structures and or fluids during excitation. Examples would include measuring the vibration of a car's body when it is attached to an electromagnetic shaker, or the noise pattern in a room when excited by a loudspeaker. Modern day modal analysis systems are composed of 1)sensors such as transducers (typically accelerometers, load cells), or non contact via a Laser vibrometer, or stereophotogrammetric cameras 2) data acquisition system and an analog-to-digital converter frontend (to digitize analog instrumentation signals) and 3) host PC (personal computer) to view the data and analyze it.

Classically this was done with a SIMO (single-input, multiple-output) approach, that is, one excitation point, and then the response is measured at many other points. In the past a hammer survey, using a fixed accelerometer and a roving hammer as excitation, gave a MISO (multiple-input, single-output) analysis, which is mathematically identical to SIMO, due to the principle of reciprocity. In recent years MIMO (multi-input, multiple-output) have become more practical, where partial coherence analysis identifies which part of the response comes from which excitation source. Using multiple shakers leads to a uniform distribution of the energy over the entire structure and a better coherence in the measurement. A single shaker may not effectively excite all the modes of a structure.[1]

Typical excitation signals can be classed as impulse, broadband, swept sine, chirp, and possibly others. Each has its own advantages and disadvantages.

The analysis of the signals typically relies on Fourier analysis. The resulting transfer function will show one or more resonances, whose characteristic mass, frequency and damping can be estimated from the measurements.

The animated display of the mode shape is very useful to NVH (noise, vibration, and harshness) engineers.

The results can also be used to correlate with finite element analysis normal mode solutions.

## Structures

In structural engineering, modal analysis uses the overall mass and stiffness of a structure to find the various periods at which it will naturally resonate. These periods of vibration are very important to note in earthquake engineering, as it is imperative that a building's natural frequency does not match the frequency of expected earthquakes in the region in which the building is to be constructed. If a structure's natural frequency matches an earthquake's frequency, the structure may continue to resonate and experience structural damage.

Although modal analysis is usually carried out by computers, it is possible to hand-calculate the period of vibration of any high-rise building through idealization as a fixed-ended cantilever with lumped masses. For a more detailed explanation, see "Structural Analysis" by Ghali, Neville, and Brown, as it provides an easy-to-follow approach to idealizing and solving complex structures by hand.

## Electrodynamics

The basic idea of a modal analysis in electrodynamics is the same as in mechanics. The application is to determine which electromagnetic wave modes can stand or propagate within conducting enclosures such as waveguides or resonators.

## References

1. ^ a b "Comparison of Modal Parameters Extracted Using MIMO, SIMO, and Impact Hammer Tests on a Three-Bladed Wind Turbine, Experimental Mechanics Series 2014, pp 185-197 [1]
• D. J. Ewins: Modal Testing: Theory, Practice and Application
• Jimin He, Zhi-Fang Fu (2001). Modal Analysis, Butterworth-Heinemann. ISBN 0-7506-5079-6.